Many questions come up in probability involving a standard deck of playing cards. Furthermore, many times card players will also want to know different probabilities for the card games they are involved in.
In this post, you will learn about probability with a deck of cards and how it works. This will include examples of probability with cards, and also how many ways a deck of cards can be shuffled and arranged. Finally, common playing card probability questions will be answered.
The 52 cards in the deck are divided into 4 suits. These suits are the Hearts, Diamonds, Clubs and Spades. The Hearts and Diamonds are the red suits. The Clubs and Spades are the black suits.
Each suit has the same 13 value cards. These cards are the Ace, Two, Three, Four, Five, Six, Seven, Eight, Nine, Ten, Jack, Queen, and King.
In probability, a deck of cards is usually 52 cards. (The Jokers are usually not included. See more at How Many Cards are in a Deck Without Jokers? to learn more about why it’s this number without the Jokers)
How Many Face Cards In a Deck?
There are 12 face cards in a deck. Each of the 4 suits gets one of each of the 3 face cards, the Jack, Queen and King. There are 6 red face cards and 6 black face cards in a deck.
Full Deck of Cards
A full deck of cards will have 13 cards in each of the 4 suits. These 13 cards are the Ace, Two, Three, Four, Five, Six, Seven, Eight, Nine, Ten, Jack, Queen and King.
Here is an image of a full deck of cards with each of the 13 cards in each of the 4 suits.
Full deck of cards
Playing Cards Probability
Let’s look at an introduction to probability with playing cards. This will give us a basic overview of the way probability works with playing cards.
Probability of a Regular Pack of 52 Cards Explained – Playing Cards Probability
Probability Examples with Cards
Next, we can look at some examples of probability with cards.
Probability Examples with Cards
We can also look at some probability examples using Venn Diagrams for more clarity.
Probability with playing cards and Venn diagrams
Face Cards in Probability
There are 12 face cards in a deck of 52 cards. (To learn more see Face Cards in a Deck) This means that the odds of drawing a face card will be 12/52, or 3/13.
The odds of drawing a non-face card will be the opposite of this, or 40/52, which simplifies to 10/13.
There are 6 red face cards and 6 black face cards in a deck. This means the odds of drawing a red face card are 6/52 or 3/26. The odds of drawing a black face card are the same, 3/26.
Shuffled Deck of Cards Probability
How Many Ways Can You Arrange a Deck?
How many ways can you shuffle a deck of cards? It’s hard to imagine, but if you shuffle a deck of cards, you are almost certainly holding a deck of cards that is in an order that has never been seen before in all history!
How many ways can you arrange a deck of cards? There are exactly 8.07×10^67 ways that a 52 card deck can be arranged.
If this were written out, it would be the number 8 followed by 67 zeros!
How Many Ways Can You Order a Deck of Cards
See how mind-boggling this number actually is in the following video.
Combinations of 52 Cards
Deck of Cards Probability Questions
What is the probability of drawing any card from a deck of cards?
The probability of drawing any random card from a deck of cards would be 1/52.
This is because you have 1 card that you can choose out of 52 options.
What is the probability of drawing an Ace from a deck of cards?
The probability of drawing an Ace from a deck of cards is 1/13.
This is because there are 4 Aces, and you have 52 total possible cards that could be drawn.
This gives you 4/52 as the probability of drawing an Ace, which is simplified to 1/13.
What is the probability of drawing a red card from a deck of cards?
The probability of drawing a red card from a deck is 1/2.
This is because there are 26 red cards out of 52 possible choices.
This gives 26 chances of selecting a red card out of 52, or 26/52. This simplifies to 1/2.
What is the probability of drawing a black card from a deck of cards?
The probability of drawing a black card from a deck is 1/2.
This is because there are 26 black cards out of 52 possible choices.
This gives 26 chances of selecting a black card out of 52, or 26/52. This simplifies to 1/2.
What is the probability of drawing a Heart from a deck of cards?
The probability of drawing a Heart from a deck of cards is 1/4.
This is because there are 13 Heart cards in a deck out of 52 possible cards.
This gives 13 chances to select a Heart out of 52 possible cards. This gives a probability of 13/52. This simplifies to 1/4.
What is the probability of drawing a Diamond from a deck of cards?
The probability of drawing a Diamond from a deck of cards is 1/4.
This is because there are 13 Diamond cards in a deck out of 52 possible cards.
This gives 13 chances to select a Diamond out of 52 possible cards. This gives a probability of 13/52. This simplifies to 1/4.
What is the probability of drawing a Spade from a deck of cards?
The probability of drawing a Spade from a deck of cards is 1/4.
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